Hoping this would be an easy to implement idea.

Basically a Transfer Chest would have 4 lines of slots but only a total of 8 slots (or however many they current have).

Opening the chest you would see 4 lines of slots and each time you add an item, the other lines of slots would lose a slot as well. So if you put 8 items in the first row, all the other rows have no open slots for new items. Maybe they keep one greyed out slot that would accept items from other rows.

Basically the idea is to allow some sorting in the transfer chest. I would use it where each row represents a different character.

Another method, maybe even easier would be add a number of inventory bags to the transfer chest.